Tuddenham and Snyder obtained the following results for 6

Maiclubk 2021-02-24 Answered

Tuddenham and Snyder obtained the following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped):
average height at \(6 \approx 3\) feet 10 inches, \(SD \approx 1.7\) inches
average height at \(18 \approx 5\) feet 10 inches, \(SD \approx 2.5\) inches, \(r \approx 0.80\)
a) Find the r.m.s. error for the regression prediction of height at 18 from height at 6. b) Find the r.m.s. error for the regression prediction of height at 6 from height at 18.

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Expert Answer

hesgidiauE
Answered 2021-02-25 Author has 16917 answers

\(\sqrt{(1-r^{2})} \cdot SD_{y}\)
a) The r.m.s. error for the regression prediction of height at 18 from height at 6: in this case:
\(\sqrt{1-0.8^2} \cdot 2.5 = \sqrt{1-0.64} \cdot 2.5 = \sqrt{0.36} \cdot 2.5 = 0.6 \cdot 2.5 = 1.5\)
b) The r.m.s. error for the regression prediction of height at 6 from height at 18:
\(\sqrt{1-0.8^2} \cdot 1.7 = \sqrt{1-0.64} \cdot 1.7 = \sqrt{0.36} \cdot 1.7 = 0.6 \cdot 1.7 = 1.02\)
Answer: a) 1.5, b)1.02

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